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Project T2: Embedded one-dimensional electron-phonon systems

Eric Jeckelmann

The aim of this project is to gain a better understanding of one-dimensional physics in
atomic wires on surfaces. We will generalize the theory of the Peierls transition driven by
the coupling between electrons and lattice distortions to take into account the peculiarities
of these systems. We will also examine the influence of the underlying substrate on the
Luttinger liquid properties of metallic wires. The signature of one-dimensional phases will
be determined for the experimental techniques. This
will facilitate the interpretation of experimental data and thus enable the identification
of one-dimensional physics in atomic wire systems. Furthermore, in collaboration with
project T1 we aim to achieve quantitative microscopic theories of the Peierls-like transition
in In/Si(111) and Luttinger liquid properties in Au/Ge(100).
Our investigations will be based on effective models for the low-energy properties of
atomic wires on surfaces. These systems can be regarded as two-dimensional arrays of
weakly-coupled chains (wires) with interacting electron and phonon degrees of freedom
which are embedded in a three-dimensional environment (the underlying substrate). The
model Hamiltonians generalize those which have been used so successfully in studies
of one-dimensional electronic systems in the previous fifty years, such as the Holstein
model and the Hubbard model. We will determine the relevant degrees of freedom and
interactions from the first-principle calculations  and the experimental data. To solve these models we will exclusively use well-established methods such as mean-field theory, quantum Monte Carlo simulations, bosonization, and density-matrix renormalization group.

(Picture: Mapping of an atomic wire with its substrate onto a ladder-like system with the wire at the edge and the other (N = 4) legs representing the substrate.)